If XYZ is at 12.50, you could buy to open a 10 Call for $3. That option controls 100 shares, so your cost is $300.

If the stock goes to 14 with a week before expiration, what will your 10 Call option be worth? That's a tricky question, because there will still be some time value left in the option. I would guess it might be worth 4.20. That would be $4 in intrinsic value, because the stock is at 14, and the option strike is at 10, plus my guess at 20c in time value.

So, your option went from $3.00 to $4.20, so your profit was (4.2-3.0)*100=$120.

If the stock dropped to 12 with a week left, your 10 Call would be worth $2, plus some time value, perhaps $2.10 total. So yes, you could sell to close your 10 Call option for $2.10. Your loss would be (3.0-2.1)*100 - $90.

Yes, to break even, you would have to be at 13 at expiration.

However, please note that in general, it is a bad idea to buy a Call option in the expiration month. Options decay at ever increasing rates, so if you are holding a long call option during expiration week, you are losing money daily.

It is a better strategy, if you are going to buy a long call, to do it with at least 45 days till expiration, and plan on selling to close the option if it gets inside 25-30 days till expiration. If you think you want to hold an option for a month, plan on buying an option that is at least 60 days till expiration, so that you can hold it for a month and still sell it before it gets to 30 days till expiration.